As the wrangling begins over how to pay for the Metropolitan Transportation Authority’s ambitious new subway rescue plan, officials offered news on Wednesday that was unlikely to make riders happy: Fares will probably rise again.

The authority’s chief financial officer, Robert E. Foran, said officials planned to raise fares for subway and bus riders in 2019 and 2021. The last fare and toll increase occurred in March, when the price of a weekly MetroCard rose by $1 to $32.

At the authority’s monthly board meeting in Lower Manhattan, Mr. Foran said the agency needed to continue to raise fares by about 4 percent every other year as part of its long-term financial plans. But some board members bristled at the biennial ritual, especially as service deteriorated.

“I think it is time now for us and our partners at the state to review or re-evaluate the every-other-year fare and toll discussion,” said Mitchell Pally, a longtime board member. “I don’t think that’s sustainable.”

Another board member, Andrew Albert, said the authority had to secure other funding streams to support operations, instead of continuing to raise fares.

“If you take these to their logical conclusion, at some point, the fare will be $10 and tolls will be $50, and I’m not sure that is sustainable,” Mr. Albert said.

The authority’s chairman, Joseph J. Lhota, said he was prepared to examine new funding sources to avoid regular fare increases.

“It was clearly the sense of the board that we need to replace the biennial fare increases with a new stream of revenue,” Mr. Lhota said in an interview.

Mr. Lhota is separately pressing Mayor Bill de Blasio to pay for half of Mr. Lhota’s roughly $800 million subway rescue plan. Gov. Andrew M. Cuomo, who controls the authority, has agreed to pay for the rest, but Mr. de Blasio has resisted giving the authority more money.

The public feud over the subway continued Wednesday, with Transport Workers Union Local 100 releasing a campaign-style television advertisement criticizing Mr. de Blasio for not agreeing to finance the plan. The ad also praised Mr. Cuomo, a frequent ally of the union, which represents thousands of subway workers.

The union said the ad was part of a six-figure campaign that would run on NY1, CNN and MSNBC. The union supports the subway rescue plan, which calls for fixing signals and tracks and hiring 2,700 workers.

“Part of what I’m trying to make clear is it begins with responsibility,” the mayor said. “The M.T.A. has to take responsibility for its own actions. The State of New York has to take responsibility for the fact it controls the M.T.A.”

Mr. Lhota, who returned to lead the authority in June to help fix the subway after an earlier stint as chairman, said he would continue to try to work with city officials to persuade them to fund the plan.

“I still think there’s a need for partnership between the city and state to come to the aid of the riders — the people of the City of New York, the constituents they have,” Mr. Lhota told reporters after the board meeting. “I’m optimistic something can happen from that.”

The budget presentation by Mr. Foran also revealed the steep costs of the agency’s contingency plans for summer repairs at Pennsylvania Station in New York — a transit headache Mr. Cuomo called the “summer of hell.” The authority is providing discounts for Long Island Rail Road riders and an array of travel options to help commuters whose lives have been disrupted by the closing of several tracks at the busy train station.

The authority expected to lose $58 million from higher expenses and lower revenue in July and August, Mr. Foran said. That includes more than $21 million in lost revenue, about $18 million for buses and $5 million for ferries.

Mr. Lhota said the agency’s approach had been working well.

“Was it a lot of money?” he asked. “Yes. Is it well worth it? Yes. Because not doing it — the catastrophe that it would have caused would have been unbearable for the entire region over all.”

A version of this article appears in print on , on Page A22 of the New York edition with the headline: Despite Subway Crisis, M.T.A. Plans to Stick to Fare Increases in 2019 and 2021. Order Reprints | Today’s Paper | Subscribe